3.3. The velocities at a point in a fluid in the Eulerian system are given by ux+y+z+s =2(x + y + z) +- 1 W = 3(x + y + z) + i Show that the displacements of a fluid particle in the Lagrangian system are x=2x-30 120 + f (x + y + zo + 1')e" - r²+++ - - y= -xo+yo-zo + (xo + yo + zo + 1)e³ - f - 38 z = −x − y + zo + (x + yo +20 + 1)e" - 11 - 11² - 2 -
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- 4. The velocity vectors of three flow fileds are given as V, = axĩ + bx(1+1)}+ tk , V, = axyi + bx(1+t)j , and V3 = axyi – bzy(1+t)k where coefficients a and b have constant values. Is it correct to say that flow field 1 is one-, flow filed 2 is two-, and flow filed 3 is three-dimensional? Are these flow fields steady or unsteady?Given the Eulerian velocity vector field: V = 3ti + xzj + ty²k Find the total acceleration of a particle av av av W дх' ду' ду Hint: u VThe velocity component in the y-direction is given as v = 3x - 4y for the steady, inviscid and two- dimensional flow of an incompressible fluid. The only body force is the gravity, g, and it acts in the negative y-direction. The density of the fluid is p. For an irrotational flow, determine a) The velocity component in the x-direction, if it is zero at the origin b) The acceleration vector: ) and c) The pressure field, if the pressure is Po at the origin d) The stream function(
- Given the eulerian velocity - vector field V(x,y,z,t) = 3ti +xzj+ty²k, find the acceleration of a particle.1.6 An incompressible Newtonian fluid flows in the z-direction in space between two par- allel plates that are separated by a distance 2B as shown in Figure 1.3(a). The length and the width of each plate are L and W, respectively. The velocity distribution under steady conditions is given by JAP|B² Vz = 2µL B a) For the coordinate system shown in Figure 1.3(b), show that the velocity distribution takes the form JAP|B? v, = 2μL Problems 11 - 2B --– €. (a) 2B (b) Figure 1.3. Flow between parallel plates. b) Calculate the volumetric flow rate by using the velocity distributions given above. What is your conclusion? 2|A P|B³W Answer: b) For both cases Q = 3µL2. A moving car, represented as a point, has a time-varying position given by z(t) = a +be² -ct and a time-varying velocity given by (1)=2b1²-6ct² where a = 2.17 m. b = 4.80 m/s², and c= 0.100 m/s. Find: (a) the car's average velocity from 2.00 to 10.0 s, (b) the car's average acceleration during the same interval. (c) the car's velocity at t = 5.0 s. (d) and the car's acceleration at the same time.
- Exercise 1 At a certain point of a body, the components of the cauchy stress tensor are given by [2 5 3 [o] 5 1 4 3 4 3 a) Find the components of cauchy traction vector tn at the point on the plane whose normal has direction (3, 1, –2). b) Find the normal and shear commponents of tn on that point.2. The velocity components expressed in m/s in a fluid flow is known to be: 2 u= 2yzt v=xy W=4xzt² Find the acceleration of a fluid particle at point, P (2m,1m,1m) when time is 2 s.For the flow of an incompressible fluid, the velocity in x-direction u = ax + by and velocity in z-direction is zero. Find velocity component in y-direction such that v = 0 at y = 0. O at
- Home Work (steady continuity equation at a point for incompressible fluid flow: 1- The x component of velocity in a steady, incompressible flow field in the xy plane is u= (A /x), where A-2m s, and x is measured in meters. Find the simplest y component of velocity for this flow field. 2- The velocity components for an incompressible steady flow field are u= (A x* +z) and v=B (xy + yz). Determine the z component of velocity for steady flow. 3- The x component of velocity for a flow field is given as u = Ax²y2 where A = 0.3 ms and x and y are in meters. Determine the y component of velocity for a steady incompressible flow. Assume incompressible steady two dimension flow1. A flow in the x-y plane is given by the following velocity field: u =3 and v=6m/s for 0The position of an object moving along an x axis is given by x = 3t - 4t? + t, where x is in meters and t in seconds. Find the position of the object at the following values of t: (a) 1 s, (b) 2 s, (c) 3 s, and (d) 4 s. (e) What is the object's displacement between t = 0 and t = 4 s? (f) What is its average velocity for the time interval from t = 2 s tot = 4 s? (g) Graph x versus t for 0SEE MORE QUESTIONSRecommended textbooks for youElements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill EducationControl Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEYElements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill EducationControl Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY